Cloaking with footprints to provide location privacy protection in location-based services

ABSTRACT

A method for using a location-based service while preserving anonymity includes receiving a location associated with a mobile node, receiving an anonymity level associated with the mobile node, computing a region containing the location of the mobile node and a number of footprints based on the anonymity level, wherein each of the footprints from a different user, and providing the region to a location-based service to thereby preserve anonymity of the mobile node. A method also allow a mobile device or its user to specify the anonymity level by selecting a public region consistent with a user&#39;s feelings towards desired privacy.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a Divisional application of U.S. Ser. No. 14/472,462 filed Aug.29, 2014, which is a Divisional application of U.S. Ser. No. 12/555,456filed Sep. 8, 2009, now U.S. Pat. No. 8,856,939, issued Oct. 7, 2014,which claims priority under 35 U.S.C. §119 to provisional applicationSer. No. 61/094,635 filed Sep. 5, 2008, all of which are hereinincorporated by reference in their entirety.

FIELD OF THE INVENTION

The present invention relates to location-based services. Moreparticularly, but not exclusively, the present invention relates toproviding privacy protection in location-based services.

BACKGROUND OF THE INVENTION

Many applications today rely on location information of users ordevices, yet disclosing such information without appropriate measurespresents heightened privacy and safety threats. Currently there is notechnique which can effectively prevent one from being identified andlocated should one's detailed movement be tracked. This lack ofprotection has greatly hindered the development and deployment of a widerange of important applications like location-based services. There isan urgent need, therefore, to develop techniques that allow users ordevices to disclose their location information as accurately as possiblefor useful applications while providing them location privacyprotection, i.e., ensuring such information cannot be used byadversaries to derive who is where at what time.

In addition, there are problems relating to a user's ability to specifya desired level of privacy protection in a meaningful way. What isneeded is a convenient and effective way for users to specify theirdesired level of privacy protection.

SUMMARY

Therefore, it is a primary object, feature, or advantage of the presentinvention to improve over the state of the art.

It is a further object, feature, or advantage of the present inventionto enable location privacy protection in location-based services viahistorical location information.

Another object, feature, or advantage of the present invention is toprovide location privacy protection in location-based services which isrobust.

Yet another object, feature, or advantage of the present invention is toprovide location privacy protection in location-based services whichallows for users to specify the level of privacy they wish to have in ameaningful way.

One or more of these and/or other objects, features, or advantages ofthe present invention will become apparent from the specification andclaims that follow. No single embodiment of the present invention needexhibit all objects, feature, or advantages of the present invention.

A spatial region with K different footprints indicates that it has beenvisited by K different people. An adversary may be able to identify allthese users, but will not know who was there at what time. Thisobservation gives us a new direction to investigate locationdepersonalization in location-based services (LBSs). We propose toleverage users' historical location samples, each being a footprint, tocloak their current location. For each location/trajectory reported forLBSs, we ensure that it has been visited earlier by at least K−1 otherusers. In contrast to existing techniques which depersonalize a user'slocation based on her current neighbors, our approach is able to providea certain level of guarantee that a user's location information, eithera single location sample or a time-series sequence of them, cannot becorrelated with restricted spaces such as home and office to derivewho's where at what time. In addition to location privacy protection,using footprints for cloaking can significantly improve cloakingresolution and allow mobile nodes to report their location only whenthey are engaged in LBSs. We present novel algorithms for singlelocation sample cloaking and trajectory cloaking, and evaluate theirperformance under various conditions using location data generated basedon real road maps. Our results show that the proposed techniques have aminimal impact on the quality of LBSs.

In addition, a feeling based privacy model for location privacyprotection is provided. Here, a user expresses her privacy requirementby specifying a public region, instead of a value of K. A spatial regionis considered a user's public region if the user feels comfortable thatthe region is reported as her current location when the user is insidethe region. For example, a shopping mall can be a user's public region,if the user does not mind that the mall is disclosed as her locationwhen she requests an LBS in it. Given a public region specified by auser, we apply the concept of entropy to measure its popularity based onthe footprints collected from the visitors of the region. Thispopularity is then used as the user's privacy requirement. For eachlocation disclosed on behalf of the user, we ensure that the popularityof this location is no less than that of the specified public region.Methods allow for a user's time-series location information to bereported as accurately as possible while ensuring that her locationprivacy requirement is always met. The method used cloaks a user'smovement on the fly without having to know the moving trajectory inadvance. As such, the method can be used in application scenarios wherea user needs to make frequent location updates along a trajectory thatis not predetermined. In addition, the method guarantees that a desiredlevel of location privacy cannot be compromised even if the distributionof users' footprints is not uniform along the trajectory.

According to one aspect of the present invention, a method for using alocation-based service while preserving anonymity is provided. Themethod includes receiving a location associated with a mobile node,receiving an anonymity level associated with the mobile node, computinga region containing the location of the mobile node and a number offootprints based on the anonymity level, wherein each of the footprintsfrom a different user, and providing the region to a location-basedservice to thereby preserve anonymity of the mobile node.

According to another aspect of the present invention, a method for usinga location-based service while preserving anonymity is provided. Themethod includes determining a base trajectory associated with a mobilenode, the base trajectory comprising at least two points, anddetermining an anonymity level, K, associated with the mobile node. Themethod further includes computing a K-anonymity trajectory using thebase trajectory, the anonymity level, and a set of other trajectories.The method further includes providing the K-anonymity trajectory to alocation-based service to thereby preserve anonymity of the mobile node.

According to one aspect of the present invention, a method for using alocation-based service while preserving anonymity is provided. Themethod includes receiving a location associated with a mobile node andreceiving an anonymity level associated with the mobile node. The methodfurther includes computing a region containing the location of themobile node and a number of footprints based on the anonymity level,wherein each of the footprints from a different user. Then the methodprovides the region to a location-based service to thereby preserveanonymity of the mobile node.

According to another aspect of the present invention, a method for usinga location-based service while preserving anonymity. The method includesdetermining a base trajectory associated with a mobile node, the basetrajectory comprising at least two points. The method further includesdetermining an anonymity level, K, associated with the mobile node andcomputing a K-anonymity trajectory using the base trajectory, theanonymity level, and a set of other trajectories. The method providesthe K-anonymity trajectory to a location-based service to therebypreserve anonymity of the mobile node.

According to another aspect of the present invention, an apparatus forproviding location-based services while preserving anonymity isprovided. The apparatus includes an anonymity server configured forreceiving a location associated with a mobile node, determining theanonymity level associated with the mobile node, computing a regioncontaining the location of the mobile node and a number of footprintsbased on the anonymity level, and communicating the region to alocation-based service to thereby preserve anonymity of the mobile node.The anonymity server may be so configured by placing instructions forperforming such steps on a computer readable media and executing thoseinstructions.

According to another aspect of the present invention, a method forproviding location-based services while preserving anonymity isprovided. The method includes determining a base trajectory associatedwith a mobile device, the base trajectory comprising at least twopoints, determining anonymity level, K, associated with the mobiledevice and computing a K-anonymity trajectory using the base trajectory,the anonymity level, and a set of other trajectories. The method furtherincludes providing the K-anonymity trajectory to a location-basedservice to thereby preserve anonymity of the mobile device. Theanonymity level may be determined by a spatial region specified by themobile device or its user.

According to another aspect of the present invention, a method forproviding location based services to a user is provided. The methodincludes providing the user with a mobile device, the mobile devicehaving a cellular transceiver and a global positioning system (gps)receiver and wherein the mobile device is configured to receive aselection of a spatial region from the user. The method further includesreceiving a selection of the spatial region from the user, computing ananonymity level associated with the user using a computer, and receivinga location associated with the mobile device. The method provides forcomputing a region containing the location of the mobile device and anumber of footprints based on the anonymity level, wherein each of thefootprints being from a different user and then providing the region toa location-based service to thereby preserve anonymity of the mobiledevice.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates one embodiment of a system architecture where a userrequests an LBS through a central anonymity server which is trusted.

FIG. 2 illustrates a footprint database.

FIG. 3 illustrates that C_(min) must be inside C_(b) (K=4).

FIG. 4 provides an example of a K-anonymity trajectory.

FIG. 5 illustrates an example of cloaking T₀ with T_(a).

FIG. 6 illustrates the effect of anonymity requirement for singlelocation cloaking.

FIGS. 7A and 7B illustrate the effect of the anonymity requirement.

FIGS. 8A and 8B illustrate the effect of trajectory length.

FIGS. 9A and 9B illustrate the effect of trajectory database size.

FIG. 10 illustrates a pyramid data structure.

FIG. 11 illustrates an example of a travel bound with people ofdifferent popular level.

FIGS. 12A-12F illustrate the impact of system parameters on performance.

FIGS. 13A-13C illustrate server and client interfaces.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 1. Introduction

Location-based services (LBSs) allow users to query useful informationsuch as nearest hotels, restaurants, and so on. While such applicationsoffer significant opportunities for a broad range of markets, a majorconcern is the potential abuse of location data collected by serviceproviders. Physical destinations such as medical clinics may indicate aperson's health problems. Likewise, regular stops at certain types ofplaces may be linked directly to one's lifestyle or politicalassociation. When location data is subject to risks such as potentialmisuse by insiders, unintentional or mistaken disclosure, encryption andpolicy-based approaches generally do not work. In the case of LBSs,users need to supply their location in order to use the services, yetthe service provider may not be trustworthy in keeping this informationsafe. The users may be informed of the policies regarding the collectionand distribution of their location data. In reality, however, theexecution of these policies is typically beyond their control and reliessolely on the service providers.

Knowing that location information may fall into a wrong hand, it isnatural and necessary for a user to withhold her true identity whenrequesting an LBS. Unfortunately, simply using a pseudonym, or not usingan identifier at all, is not sufficient because a user's location itselfmay be correlated with restricted spaces such as home and office toreveal her real-world identity. Even if an individual location samplemay not be linked to a subject, the accumulation of location data willeventually reveal the user. This problem has motivated a series ofresearch efforts on location depersonalization (e.g., [10], [8], [19],[16], [5], [3], [15], [6], [9]). Instead of disclosing a user's accuratelocation, the basic idea of the proposed techniques is to compute acloaking box which contains the user and at least K−1 others, and reportthis box as the user's location in requesting a LBS. Since each cloakingbox contains a certain number of current users, this strategy provides adesired level of guarantee that a cloaking box cannot be linked to somespecific user.

The above techniques can support anonymous uses of LBSs, but notlocation privacy protection. Given a cloaking box submitted at time t,an adversary may not know which node requests the service, but knows forsure that the service requestor is inside the area at that time. Inparticular, by correlating with restricted spaces, the adversary has thepotential to identify all nodes that were inside the cloaking box attime t. This presents serious privacy threats, because “where you areand who you are with are closely correlated with what you are doing”[18]. In addition to location privacy leak, these existing techniqueshave the following limitations:

-   -   They require latest location information from all mobile nodes        in order to compute cloaking boxes. In reality, nodes not        needing LBSs may not be willing to disclose their location.        Excessive location updates from a large number of mobile nodes        also present overwhelming communication and processing        bottlenecks on the server side.    -   Besides the practicality and scalability issues, another problem        is, when the node is in an unpopulated area, its cloaking box        can be very large. A fine cloaking resolution is critical for        the quality of a LBS. One can compute a smaller cloaking box        after more nodes come nearby. This approach, however, requires        to delay a service request and the delay is indefinite.    -   Finally, existing techniques cannot be used in continuous LBSs,        wherein users report their location frequently. Simply ensuring        each reported location is a cloaking box containing at least K        nodes does not give a user K-anonymity protection. A time-series        sequence of cloaking boxes form a trajectory that may reveal a        user if, for instance, it links to the user's home and office.

Our research aims at addressing the above problems, with an emphasis onlocation privacy protection. Specifically, we want to prevent a user'slocation information, either a single location sample or a time-seriessequence of them, from being correlated with restricted spaces to derivewho's where at what time. Our key idea is to cloak users' currentlocation with their historical location samples, each called afootprint. For each location or trajectory reported in service requests,we ensure that it has been visited earlier by at least K−1 other users.Given a spatial region with K different footprints, an adversary may beable to identify all corresponding users, but will not know who wasthere at what time. With this basic idea in place, we present efficientalgorithms for single location cloaking and trajectory cloaking. For theformer, which depersonalizes a user's current position, we propose anefficient algorithm that can find the minimum bounding circle thatbounds the user and at least K−1 others. The latter is to depersonalizea user's time-series location samples. To our knowledge, no practicalsolution can be found for this purpose in literature. We give a formaldefinition of K-anonymity trajectory (KAT) and address the challenges ofcomputing such trajectories with cloaking resolution that is as fine aspossible. The performance of our techniques is studied under variousconditions using location data synthetically generated based on realroad maps.

The rest of this description is organized as follows. In Section II, wereview related works in more detail. In Section III, we give an overviewof our system model. The proposed techniques for single locationcloaking and trajectory cloaking are presented in Section IV and V,respectively. The proposed techniques are evaluated in Section VI. Weconclude in Section VII.

2. Related Work

Anonymous Uses of LBSs:

Gruteser and Grunwald first investigated this problem [10] and proposedreducing location accuracy along spatial and/or temporal dimensions foranonymity protection. When a client requests a service, the proposedscheme computes a cloaking box that contains the client and at least K−1others, and then uses this cloaking box as the client's location torequest the service. If the resolution of a location is too coarse forquality services, temporal cloaking is applied, i.e., delaying a user'sservice request. When more mobile nodes come near to the user, a smallercloaking area can then be computed. This basic concept has been improvedby a series of works. Gedik and Liu [8] considered minimizing the sizeof the cloaking boxes, a factor critical for the quality oflocation-based services, and allowing users to specify their own valueof K. The techniques proposed in [19], [16], and [5] address thechallenges of processing location-dependent queries with location ofreduced resolution. Preventing an adversary from identifying a subjectbased on her moving pattern was considered in [3] and [15]. The proposedtechniques cloak a client's position using the neighbors that have beenclose to the client for some time period. All these techniques rely on acentral anonymity server, which tracks the movement of mobile nodes andcomputes cloaking boxes upon requests. Location cloaking in fullydistributed mobile peer-to-peer environments was investigated by Chow etal [6]. Assuming mobile nodes trust each other, the proposed techniquelets mobile nodes exchange location information and collaborate incomputing cloaking boxes. More recently, Ghinita et al proposed adistributed cloaking algorithm [9] which guarantees service anonymityeven if the adversary knows the exact locations of all users. Theseexisting works, as mentioned in the introduction, aim at supportinganonymous uses of LBSs, but not location privacy protection.

Trajectory Perturbation:

Beresford and Stajano first investigated the problem of trajectoryperturbation and proposed the concept of mix zone [2]. A mix zone isdefined to be a spatial region in which a mobile node does not reportits location. When there are multiple nodes inside the same mix zone,they exchange their pseudonyms. After exiting the mix zone, these nodesstart to use new pseudonyms in location updates, making it hard for anadversary to link incoming and outgoing paths of these nodes. While thisapproach relies on a set of pre-defined spatial regions for pseudonymexchange, the path confusion algorithm proposed by Hoh and Gruteser [12]allows mobile nodes to switch their pseudonyms when their paths areclose to each other, say, within some threshold. Another strategy theyproposed is to ensure that the time interval between two consecutivelocation reports is long enough so that each can be considered as anindependent event [14]. These approaches reduce, but cannot prevent,location privacy risks. A partial trace, or just a single locationsample, can be sufficient for an adversary to identify a user, thusknowing her whereabouts.

Privacy Protection in Opportunistic Sensing and Monitoring:

Kapadia et al proposed a framework [17][7] that allows sensor-equippedmobile devices to report context information (e.g., traffic conditions,pollution reading) from their vicinity without risking their owners'location privacy. The system partitions the network domain into manytiles, each being a region that K users typically visit within a shorttime interval, and lets each node report its location at a granularityof tiles. It is unclear, though, how mobile nodes are updated with thelatest tessellation information. Moreover, the proposed system assumesthat each report is an independent event. In parallel to this work, Hohet al proposed a system for privacy-preserving traffic monitoring basedon the concept of virtual trip lines (VTLs) [13]. A VTL is a geographicmarker that indicates where a vehicle needs to make a traffic report.For privacy protection, these markers are placed to avoid particularlysensitive areas. Their distances are also made large enough to prevent auser's consecutive location updates from being re-linked as atrajectory. This approach cannot be used for location privacy protectionin location-based services because the placement of VTLs ispre-determined.

3. System Overview

Public areas like parks and highways are naturally depersonalizedspatial regions—they are not private property like home and office whichcan reveal a subject's identity; and such areas are characterized by alarge number of visits by different people at different times. In lightof this observation, we propose to leverage users' historical locationsamples to cloak their current location. Specifically, for eachlocation/trajectory reported for LBSs, we ensure that it has beenvisited earlier by at least K−1 different users. From an adversary'sperspective, any of them could be the one that presents in the area atthe service time. As such, this strategy provides a certain level oflocation privacy protection for the service users. In this section, wepresent an overview of the proposed system.

Similar to existing work (e.g., [10], [8], [19]), our system lets mobilenodes receive LBSs through an anonymity server, which is considered partof trusted infrastructures, as depicted in FIG. 1. For LBSs that requireuser authentication (e.g., for service charges), we assume anonymousauthentication (e.g., [11], [23], [20]) is used. These schemes apply theconcept of blind signature and allow a service provider to verify auser's legitimacy without having to request her true identity.

As shown in FIG. 1, a system 10 is provided. The system 10 includes atrusted cellular infrastructure subsystem 14 and an untrusted facilitiessubsystem 24. Mobile devices such as device 12A and 12B, each of whichincludes a GPS receiver and a cellular transceiver communicate with abase station 16. The base station 16 is in operative communication withan anonymity server 18 such that the base station can send location andrequest data 20 to the anonymity server 18 and the anonymity server 18can respond with an answer 22. The anonymity server 18 may beoperatively connected to a footprint database 19. The anonymity server18 is also in operative communication with untrusted facilities 24. Forexample, the anonymity server 18 may send a cloaked region and request26 through the internet 30 or other network to a location based serviceserver 32 or 32B.

We assume the adversaries have access to anonymous location datacollected by LBSs and are interested in finding who is where at whattime by correlating such information with restricted spaces such officeand home addresses. For LBSs, which may involve a large number of usersand have a global coverage, such restricted space identification isprobably the most realistic and economic way for location privacyintrusion. Unlike existing cloaking techniques, we do not considerobservation attack [10]. If an adversary has direct observation over theregion where a user locates, the user does not have location privacyanyway.

We also assume that the anonymity server is managed by some cellularservice provider, through which mobile users have access to wirelesscommunications. The cellular service provider offers anonymizationservices as a value-added feature to their clients, and supplies theanonymity server with the initial footprint database for cloaking. Thelocation samples in the database may be collected from clients' regularphone calls. If such an initial database does not exist, we assume alocation sampling phase, during which mobile nodes report their locationperiodically to the anonymity server. Unlike existing techniques, suchperiodic location update is no longer needed after the sampling phase,which may last only a short time period (e.g., a few days). Morelocation data can be obtained from mobile nodes in their requests ofLBSs and will be subsequently added to the database to improve cloakingresolution. Hereafter, we will use terms location sample and footprintinterchangeably. Recall that a trajectory is a time-series sequence offootprints collected from a same user. Thus, the database can beconsidered as a trajectory repository.

Today's localization technologies allow cellular service providers todetermine the position of a caller within a radius of 50 to 300 meters.In contrast, a GPS-enabled mobile device can detect its own positionmore precisely, up to 10 meter accurate. Due to this imperfectpositioning, we use a spatial region, a circular region in particular,to represent each location sample. A rectangle can also be used torepresent a location sample. However, rectangles of different shapes canhave the same area, making it less desirable for cloaking.

For efficient retrieval of location data, we index the footprintdatabase using a simple grid-based approach, as illustrated in FIG. 2.We partition the network domain recursively into cells in a quad-treestyle. Unless a cell is already at its minimal size (our implementationsets each cell to be at least 200×200 meter²), it is split if the numberof users who have footprints inside it exceeds some threshold. For eachcell, we maintain a cell table, which stores a list of pointers thatlink to the trajectories which have at least one footprint that overlapswith the cell. Specifically, each tuple of a cell table is a record of(uid, tlink), where uid is the ID of a mobile node which traverses thiscell, and tlink is a pointer that links to the node's trajectoryinformation. Thus, given a cell, we can efficiently retrieve thetrajectories that pass through the cell. As shown in FIG. 2, a databasedomain 40 is provided. A cell table 42 with pointers and links isprovided, the links pointed to a table 44 of trajectories.

Supporting an Instant LBS:

To request an instant LBS, a mobile node reports its current location cand a desired anonymity level K to the anonymity server. In response,the server computes a circular region that contains c and K−1footprints, each from a different user, and exports this region to theprovider of the LBS. Based on this location information, the providerdelivers the requested services (e.g., query results) to the anonymityserver, which then forwards to the service user.

Supporting a Continuous LBS:

To receive a continuous LBS, a user reports the anonymity server a basetrajectory T₀={c₁, c₂, . . . , c_(n)}, where c_(i) is a location sampleon the trajectory along which the user will move. For better quality ofservices, the user may choose to have more location samples on the basetrajectory. The user may also let the anonymity server generate thetrajectory by giving a starting position and a final destination. Givenan anonymity level K and a base trajectory T₀, the server selects fromthe footprint database K−1 other users' trajectories, each having atleast n footprints, and uses them to cloak T₀. The cloaking procedurewill generate a K-anonymity trajectory (KAT) T={C₁, C₂, . . . , C_(n)}.By covering T₀ and footprints from at least other K−1 nodes, T canprovide the user K-anonymity protection. A formal definition of KAT willbe given later. After computing T, the server contacts the provider ofthe requested LBS to start a service session. As the node moves alongthe base trajectory T₀, it reports to the server whenever it arrives atc_(i). In response, the server exports the corresponding C_(i) torequest the service on behalf of the user. When the service sessionterminates, the location data reported by the service user is added tothe footprint database for future cloaking.

4. Single Location Sample Cloaking

For instant LBSs, a mobile user N needs to report its location c and adesired anonymity level K. In response, the anonymity server computes aK-anonymity area (KAA) and uses this region to request the service onbehalf of the client. For the sake of service quality, the size of theKAA should be as small as possible. In this section, we present anefficient algorithm for finding the minimum bounding circle (MBC) thatbounds N and at least K−1 other nodes. Hereafter, we will use termsfootprint and node interchangeably. To facilitate our discussion, we useC_(min) to denote this MBC, C_(a) a bounding circle that contains N andat least K−1 other nodes, and C_(b) the circle centered at N with aradius that is two times that of C_(a). Also, given a circle C, wedenote its radius as C.R. These notations are illustrated in FIG. 3. Ouralgorithm of searching C_(min) is based on the observation that C_(min)must be bounded by C_(b). By its definition, C_(a) contains K footprintsincluding N. Since C_(a) is a candidate of C_(min), C_(min) must be nolarger than C_(a), i.e., C_(min).R≦C_(a).R. Since both C_(min) and C_(a)contain N, the distance between any point in C_(min) and Ns positionmust not be larger than 2·C_(a).R. As a result, C_(min) must be insideC_(b).

The problem now is to find a C_(a) with a small radius. This can be donein different ways, depending on how the footprints are indexed. Forinstance, if R-tree is used, we can find Ns K−1 nearest neighbors anduse the MBC that bounds N and these K−1 nodes as C_(a). Existingtechniques (e.g., [21]) can find KNN at a cost of O(K log K), assuminguniform node distribution. If a quad-tree is used (e.g., see FIG. 2), wecan choose a C_(a) as follows. First, we find the cell where N locatesand mark this cell as the searching box. If the number of nodes insidethe searching box is less than K, we expand the searching box byincluding its adjacent cells. This process is repeated until thesearching box contains at least K nodes. The number of nodes in thesearching box can be approximated at O(K). Since each node is countedonly once, finding the searching box costs O(K). Then, among thesenodes, we find K−1 nodes that are nearest to N and set C_(a) to be theMBC that bounds these K−1 nodes and N, and this computation has a costof O(K log K). Thus, the total cost of this step is O(K log K).

After locating a C_(a), we then determine C_(b) and retrieve all nodesinside C_(b). Let S be the set of these nodes and |S| the number ofthem. As the area of C_(b) is 4 times of that of C_(a), the number ofnodes inside C_(b) can be estimated as O(K), assuming uniform nodedistribution. Given C_(b) and the set of nodes inside it, we nowconstruct the candidates for C_(min) and then select the one that hasthe smallest radius as C_(min). Since C_(min) is the minimum circle thatcontains N and at least K−1 other nodes (the MBC may contain more than Knodes when there are no less than 4 nodes on the border of the circle),there must have at least two nodes on the circle line of C_(min). Thus,we can classify C_(min)'s candidates into two categories.

A candidate in the first category has exactly two nodes on its circleline. The candidate is the actually the circumscribed circle of theconvex hull of the nodes inside. Thus, in this case, the two nodes mustform a diameter of the candidate. Otherwise, there must exist a smallercircle which contains these nodes. Such candidates can be enumerated byconsidering all possible pairs of the nodes inside C_(b). Given a pairof nodes, we construct the circle with the two nodes as its diameter.The circle is a valid candidate if it contains N and at least K−1 othernodes. Among all valid candidates, we find the one that has the smallestdiameter. Let this candidate be C. Given a set of nodes S, there aretotally

$\quad\begin{pmatrix}{S} \\2\end{pmatrix}$different pairs of nodes. In addition, it takes O(K) time to verify acandidate contains at least K nodes. Thus, the computational cost inthis step is O(K³).

A candidate in the second category has at least three nodes on itscircle line. Note that any three nodes can form a triangle in atwo-dimension domain (as long as they are not on the same line), and atriangle can form only one circumscribed circle. Thus, we can enumerateall possible triple nodes in S. For each triple, we construct thecircumscribed circle formed by the three nodes. If the circle contains Nand at least K−1 other nodes, it is a valid candidate. Again, among allvalid candidates, we find the one that is smallest. Let this candidatebe C. Since the number of possible triples is

$\begin{pmatrix}{S} \\3\end{pmatrix},$the computation cost in this step is O(K⁴).

Finally, we compare C with C′, and the smaller one is C_(min). Since thetotal cost of the entire process is O(K)+O(K³)+O(K⁴)=O(K⁴), the abovealgorithm finds C_(min) in a polynomial time.

5. Trajectory Cloaking

For continuous LBSs, a user needs to report a base trajectory T₀={c₁,c₂, . . . , c_(n)}. In response, the anonymity server will compute a newtrajectory T={C₁, C₂, . . . , C_(n)} that can provide the userK-anonymity protection. For this purpose, T must cover T₀. In addition,it must also cover footprints from at least K−1 trajectories (fromdifferent users), which we will refer to as additive trajectories. Letthese trajectories be T₁, T₂, . . . , T_(K−1), and T_(j)={a_([j,1]),a_([j,2]), . . . , a_([j,m) _(j) _(])}, where 1≦j≦K−1 and m_(j) denotesthe number of footprints in T_(j). We give a formal definition ofK-anonymity trajectory (KAT) as follows.

Definition 1: T is a KAT of T₀, if for each circle C_(i) in T₀, thefollowing conditions are satisfied:

-   1) C_(i) covers c_(i) in T₀, i.e., c_(i) ⊂C_(i);-   2) C_(i) covers at least one footprint in each additive trajectory;-   3) For any C_(i) and C_(i+1), there exist two footprints a_([j,x])    and a_([j,y]) in each additive trajectory T_(j) such that a_([j,x])    ⊂C_(i), a_([j,y]) ⊂C_(i+1), and x<y.

The first two conditions ensure that each circle in T covers at least Klocation samples, each in a different trajectory. Given an additivetrajectory T_(j), it is not necessary to have all of its footprintscovered by T in order to provide K-anonymity protection to T₀. Instead,we just need to make sure that T covers at least n footprints that arein the same order as they appear in T_(j). The third condition in theabove KAT definition is to guarantee this requirement. FIG. 4illustrates an example of KAT, where K=3.

Given a trajectory T={C₁, . . . , C_(n)} we define its resolution to be

${{T} = \frac{\sum\limits_{i = 1}^{n}\;{{Area}\mspace{14mu}( C_{i} )}}{n}},$where Area(C_(i)) denotes the area of spatial region C_(i). For qualityof services, a KAT's resolution needs to be as fine as possible. Given adatabase of N trajectories, there are

$\quad\begin{pmatrix}N \\{K - 1}\end{pmatrix}$different trajectory sets with cardinality K−1. For each of these sets,its K−1 trajectories can be used as the additive trajectories to cloakbase trajectory T₀. Given a set of K−1 additive trajectories, differentorders of cloaking will also result in different KATs. Enumerating allpossible combinations allows us to find the KAT with the best cloakingresolution, but this would require intensive computation. In thefollowing subsections, we first discuss how to cloak T₀ with onetrajectory, and then apply the proposed algorithm to cloak T₀ with a setof K−1 trajectories. Finally, we discuss how to select a small set oftrajectories for cloaking from a potentially large number of trajectorycandidates.5.1. Cloaking One Additive Trajectory

Consider cloaking T₀ with an additive trajectory T_(a). Let T₀={c₁, c₂,. . . , c_(n)}, T_(a)={a₁, a₂ . . . , a_(m)}, where n≦m, and T={C₁, C₂,. . . , C_(n)} be the cloaking result. For each circle C_(i) in T, itneeds to contain c_(i) and at least one footprint in T_(a). Thus, tominimize cloaking area, we can set C_(i) to be the minimum boundingcircle (MBC) that contains c_(i) and some footprint in T_(a). When afootprint in T_(a) is selected to create the MBC for C_(i), we call thisfootprint C_(i)'s pivot. Because of the ordering constraint of KAT, notevery footprint in T_(a) can serve as C_(i)'s pivot. To circumvent thisproblem, we can create a set of pivots by selecting n footprints fromT_(a) and using them as pivots based on their index number as follows.Let this set of n footprints be {a_(p) ₁ , a_(p) ₂ , . . . , a_(p) _(n)}, where p₁<p₂< . . . <p_(n); then for all 1≦i≦n, a_(p) _(i) is used asC_(i)'s pivot. The cloaking trajectory generated by this approach mustbe a KAT. The first two conditions are satisfied because C_(i) is theMBC that bounds c_(i) and its pivot, a footprint selected from T_(a).The third condition is also satisfied because the pivots included in Tare in the same order as they appear in T_(a).

The challenge is how to select a set of pivots that can result in thebest cloaking resolution. Given a set of pivots {a_(p) ₁ , a_(p) ₂ , . .. , a_(p) _(n) }, we have T={MBC(c₁,a_(p) ₁ ), MBC(c₂,a_(p) ₂ ), . . . ,MBC(c_(n),a_(p) _(n) )}, where MBC(c_(i),a_(p) _(i) ) denotes theminimum bounding circle that bounds c_(i) and a_(p) _(i) . To find Twith the best resolution, we can find all different sets of pivots, andfor each set, compute the corresponding T's resolution. Since there aretotally)

different sets of pivots, such exhaustive search may not be feasible inpractice. To address this problem, we develop a simple yet effectiveapproach to generate pivots for each C_(i), starting from i=1, asfollows. For C₁, we select its pivot from the following m−n+1candidates: a₁, a₂, . . . , and a_(m−n+1). For each candidate, wecompute the MBC that bounds this candidate and c₁. The candidate thatresults in the smallest MBC is then selected as C₁'s pivot a_(p) ₁ . Leta_(p) ₁ be the footprint selected as C₁'s pivot, where 1≦p₁≦m−n+1. Then,we select C₂'s pivot from the following m−n+2−p₁ candidates: a_(p) ₁ ₊₁,. . . , and a_(m−n+2). Again, for each of these candidates, we computethe MBC that bounds this candidate and c₂, and then select the one withthe smallest MBC as C₂'s pivot. Suppose a_(p) ₂ is selected as C₂'spivot, where p₁+1≦p₂≦m−n+2. We then select C₃'s pivot from the followingm−n+3−p₂ candidates: a_(p) ₂ ₊₁, . . . , and a_(m−n+3), based on theircorresponding MBCs (with c₃). The same procedure is used to select thepivot for each of the rest of the circles in T. The complexity of thisheuristic algorithm is O(m).

When determining a pivot, it is possible that multiple candidates resultin the same smallest MBC. In this case, the one with the smallest indexis chosen as the pivot. This would give more candidates choices whenselecting the next pivot. It is worth mentioning that the aboveprocedure selects each pivot from a certain range of footprints inT_(a). For C₁, its pivot is selected from T_(a)'s first m−n+1footprints. For all i>1, C_(i)'s pivot is selected the range from a_(p)_(i) ⁻¹+1 to a_(m−n+i). The pseudo code of the cloaking procedureCloak(T₀, T_(a)) is given Algorithm 1. To illustrate this process, weuse an example shown in FIG. 5. T₀ and T_(a) have 4 and 9 locationsamples, respectively. For C₁, its pivot can be selected from a₁ to a₆.Since MBC(c₁,a₂) is the smallest, a₂ becomes C₁'s pivot. For C₂, we canthen select its pivot from a₃ to a₇. After selecting a₄ as C₂'s pivot,we proceed to select C₃'s pivot, which has four candidates ranged froma₅ to a₈. Note that a₆ is chosen as the pivot although MBC(c₃,a₆) andMBC(c₃,a₇) have the same size. As a result, C₄ can have two candidates,a₇ and a₈, to select its pivot.

Algorithm 1 Cloak (T₀, T_(a))  1: p ← 0  2: for 1 ≦ n do  3: M ← ∞  4:for p < i ≦ m − n + j do  5: if M > Area(MBC(c_(j), a_(i))) then  6: M ←Area(MBC(c_(j), a_(i)))  7: p′ ← i  8: end if  9: end for 10: C_(j) ←Area(MBC(c_(j), a_(p′))) 11: p ← p′ 12: end for 13: T ← {C₁, C₂, ...,C_(n)}5.2. Cloaking K−1 Additive Trajectories

With Cloak(T₀, T_(a)) in place, we now consider how to generate a KATfor T₀, given a set of additive trajectories S. Let S={T₁, T₂, . . . ,T_(s)}, where s≧K−1, and let T_(i)={a_([i,1]), a_([i,2]), . . . ,a_([i,m) _(i) _(])}, where 1≦i≦s and m_(i) denotes the number offootprints in T_(i). To generate a KAT for T₀, we need to cloak T₀ withK−1 additive trajectories. Clearly, choosing different additivetrajectories can have vastly different cloaking results. Even with afixed set of K−1 additive trajectories, the order of cloaking can alsoaffect the cloaking resolution of the cloaking results.

To avoid exhaustive search, we propose two heuristic approaches, Linearand Quadratic. The former incurs less computation costs, but the lattercan lead to better cloaking results. Linear works as follows. For eachtrajectory T_(i) in S, it calls Cloak(T₀, T₁) to generate a cloakingtrajectory, which we will denote as

. If

has a better resolution than

we say T_(i) is closer to T₀ than T_(j). The trajectories in S are thensorted based on their distance to T₀ in ascending order, and the firstK−1 trajectories (which are closest to T₀) are selected as T₀'s additivetrajectories. Let these sorted trajectories be

, . . . ,

, where

is closer to T₀ than

for all 1≦i<j≦K−1. The K−1 trajectories are then used to cloak T₀ one byone recursively. Specifically, T₀ is first cloaked with

. The cloaking result is considered as a new base trajectory and cloakedwith

. The new cloaking result is then cloaked with

and so on so forth until all K−1 trajectories are added. We call thisalgorithm Linear as it calls Cloak(T₀, T_(i)) s+K−1 times. Its pseudocode is given in Algorithm 2.

Algorithm 2 Linear(T₀, S)  1: {S = {T₁, T₂, ..., T_(s)}}  2: for 1 ≦ i ≦s do  3: T_(i) ₍ ← Cloak(T_(0,) T_(i))  4: calculate |T_(i) 

 5: end for  6: S′ ← Sort S in ascending order based on distance to T₀ 7: T ← T₀  8: {Supposes S′ = {T₁ ₍₍ ,T₂ ₍₍ ,...,T_(s) ₍₍ }}  9: for 1 ≦i ≦ K − 1 do 10 T ← Cloak (T, T_(i) ₍₍ ) 11 end for 12 return T

In Linear, additive trajectories are selected based on their distance toT₀. The distance also determines the order of cloaking. This simplestrategy falls short in some cases because it does not consider thespatial relationships among the additive trajectories. This problem isaddressed by Quadratic at a higher computation cost. This scheme alsohas K−1 iterations, and in each iteration, it selects a new additivetrajectory to cloak the trajectory, say T, which is generated in theprevious iteration. However, the selection of the new additivetrajectory is based on its distance to T, instead of T₀. Initially, T isset to be T₀. In each iteration, it calls Cloak(T, T_(j)) for each T_(j)in S. Among all generated trajectories, the one with the best resolutionis set to be T, and the corresponding T_(j) is removed from S. Afterrepeating this cloaking and selecting process K−1 times, T is output asT₀'s KAT. In the above approach, procedure Cloak(T₀, T_(a)) is called

$( {K - 1} ) \cdot ( {s - \frac{K - 2}{2}} )$times. The pseudo code for Quadratic is given in Algorithm 3.

Algorithm 3 Quadratic(ro, S)  1: {S = {T₁, T₂, ..., T_(s)}}  2: T ← T₀ 3: for 1 ≦ i ≦ K − 1 do  4: for all T_(j   ,  )S do  5: T_(j) ₍ < Cloak(T,T_(j) )  6: calculate |T_(j) 

 7: end for  8: compare T_(j) 

 for all T_(j   ,  )S  9: T″ ← the trajectory that is closest to T 10 T← Cloak(T, T″) 11 S ← S − T″ 12 end for 13 return T5.3. Selecting Additive Trajectory Candidates

In both Linear and Quadratic, the entire set of trajectories S isscanned in the process of selecting K−1 additive trajectories. Since thenumber of trajectories recorded in the footprint database can be verylarge, it is necessary to create a small set of additive trajectorycandidates before starting a cloaking process. Obviously, only thosetrajectories close to the base trajectory should be considered as thecandidates. In our implementation, we use the following approach tobuild a set of additive trajectory candidates given a base trajectoryT₀. We first find out all cells that overlap with T₀'s location samples.These cells are marked as searching boxes. According to their celltables, we then retrieve the trajectories that traverse through all ofthese cells. If the total number of these trajectories is less than K−1,we expand the search scope by merging each searching box and itsadjacent cells together as a new searching box. For the new searchingboxes, we retrieve the set of trajectories that pass through them. Thisprocess is repeated until the cardinality of the trajectory set is atleast K−1, which are then chosen as the additive trajectories togenerate KAT. Suppose it takes i rounds to find a sufficient number ofadditive trajectories. The searching box of each location sample in T₀would contain (2i−1)² cells. Given n location samples in T₀, at most(2i−1)²n cells will be accessed in the processing of selecting additivetrajectories, wherein the maximal value (2i−1)²n incurs when the nsearching boxes do not overlap.

6. Performance Study

In this section, we evaluate the performance of the proposed techniques.We modify the Network-based Generator of Moving Objects [4] to generatemobile nodes and simulate their movement on the real road map ofOldenburg, Germany, a city about 15×15 km². We extract four types ofroads from the road map, primary road (interstate expressway), secondaryroad (state road), connecting road and neighborhood road as defined incensus TIGER/Line [1]. In our simulation, mobile nodes change theirspeeds at each intersection based on a normal distribution determined bythe road type. The mean speeds and the standard deviations of movingspeeds for each road type are listed in Table I. We generate a footprintdatabase that contains a certain number of trajectories with randomlyassigned user IDs. These trajectories are indexed using the grid-basedapproach discussed in the system overview section.

For single location sample cloaking, we compare our techniques with abasic scheme that cloaks using real-time neighbors' locationinformation; for trajectory cloaking, we evaluate the proposed twoapproaches, namely Linear and Quadratic. We are mainly interested in thepotential impact of a cloaking technique on the quality of LBSs. Forthis purpose, we select cloaking range, defined to be the average radiusof cloaking circles in a KAT, as our performance metric.

TABLE I TRAFFIC PARAMETERS Road type Mean speed Standard deviationPrimary 100 km/h  20 km/h Secondary 60 km/h 15 km/h Connecting 45 km/h10 km/h Neighborhood 30 km/h  5 km/h6.1. Single Location Sample Cloaking

In this study, we compare the performance of two schemes,footprint-based cloaking (FC) and neighborhood-based cloaking (NC). Theformer is what we propose, whereas the later is a basic approach thatcloaks a node's position based on the location of its currentneighboring nodes. In each simulation, we generated 5000 mobile nodesand randomly distributed them in the map. We randomly selected 200mobile nodes, each submitting a service request. We varied the value ofK from 5 to 100, and investigated the impact of anonymity requirement(i.e., the value of K, as requested by users) on the performance of thetwo techniques. The performance results are plotted in FIG. 6. It showsthat NC performs many times worse than FC. In particular, as Kincreases, the average cloaking range under NC increases dramatically.In this scheme, a larger value of K means more mobile nodes need to beincluded in a cloaking circle. Since the users are randomly distributedin the network, the average size of cloaking circles increasesproportionally with respect to the increase of K. In contrast, theperformance of FC is much less sensitive to the value of K, because thesize of a cloaking circle is determined by the number of differentfootprints that can be found nearby. As the figure shows, the averagesize of cloaking circles computed with this scheme at K=100 is less thanthat by FC at K=5. Since the size of a cloaking circle determines thequality of a LBS a user receives, cloaking with footprints can provide adesired level of anonymity protection, yet have a significant lessimpact on the providers of LBSs, as compared to the tradition approach.

6.2. Trajectory Cloaking

For trajectory cloaking, we evaluate the performance of the two proposedtechniques. For comparison purpose, we have also implemented a Baselineapproach, which uses the current position of mobile nodes for cloaking.Given a node N, this scheme finds the MBC that contains N and at leastK−1 others and uses it as N's first cloaking circle. Among the nodes inthe circle, K−1 nodes that are nearest to N are selected as Nscompanies. From then on, each time N makes a location update, Baselinefinds the MBC that contains N and these K−1 companies and reports thisMBC as N's cloaking circle. For each simulation, we generate a set ofLBS requests. Each request contains a user's ID, the start anddestination of a travel plan, and a required anonymity degree. The startand destination are randomly selected from the neighborhood areas in themap, and the fastest path between them is picked as the user's expectedroute. We select a location sample every 100 meters along the route andthese samples form the user's base trajectory. Other parameters used inour study are given in Table II. In the following subsections, we reporthow the performance of the three techniques is affected by variousfactors.

TABLE II EXPERIMENT SETTINGS parameter range default unit Number ofusers 5000 5000 unit Anonymity level 10-20  15 unit Trajectory databasesize 100K-300K 200K unit Base trajectory length 3K-8K  5K meter Servicerequest number  200  200 unit Minimum cell size 50 × 50 50 × 50 Meter²

1) Effect of Anonymity Level Required:

In this study, we investigated the impact of anonymity requirement(i.e., the value of K, as requested by users) on the performance of thethree techniques. The footprint database used in this study contains200,000 trajectories. We generated 200 service requests, each having aroute of 5000 meters with 500 meters deviation. The value of K is variedfrom 10 to 20. The performance results are plotted in FIG. 7. When Kincreases, the average cloaking range under all schemes increases, asshown in FIG. 7A. However, Baseline always results in the largestcloaking ranges, about 10 times more, as compared to the other two.Given a service user, Baseline needs to ensure that all cloaking circlesgenerated for the user include a common set of K nodes. Since thesenodes may move on different directions, the cloaking range becomesincreasingly large. When K is larger, the cloaking results alsodeteriorate quicker. As for the other two schemes, FIG. 7A shows thatQuadratic always outperforms Linear. This, however, is achieved at amore computation overhead.

FIG. 7B shows the average cloaking range on different types of roads.The primary and secondary roads are popular. A small space on such roadsmay have a large number of footprints from different users. Thus, thecloaking range is not very sensitive to the value of K. As the figureshows, the corresponding two curves are almost flat. In contrast, theconnecting roads and neighborhood roads are less popular and have a muchless number of trajectories passing through them. When K increases, theaverage cloaking range increases sharply, since a cloaking trajectorymay have to cover different roads in order to guarantee a sufficientlevel of anonymity protection. In reality, a user's route typicallycovers different types of roads, and a large portion of the route is onhighways. Since it is the cloaking circles along these popular areasthat dominate the average cloaking range, cloaking with footprintsallows users to select a large K for anonymity protection whilemaintaining good cloaking results.

2) Effect of Base Trajectory Length:

In this study, we investigated the impact of length of base trajectorieson the performance of the three techniques. The footprint database usedin this study contains 200,000 trajectories. In each simulation run, weset K=15 and generated 200 base trajectories. The average length ofthese base trajectories is varied from 3000 meters to 8000 meters. Theperformance results are shown in FIGS. 8A-8B. Under all three schemes,the average cloaking range increases as the trajectory length increases,as showed in FIG. 8A. However, Baseline performs much worse as comparedto its counterparts. It is worth mentioning that the cloaking rangeunder this scheme increases sharply as the base trajectory lengthincreases. This again convinces that cloaking with neighbors' locationis untenable for anonymity protection in continuous LBSs. As for Linearand Quadratic, both are little sensitive to the base trajectory length.As explained in the previous study, when a large portion of a user'strajectory is on highways, the cloaking circles on the highwaysdetermines the average cloaking ranges. Since our simulation uses thefastest path between a start and a destination as a user's route, whenthe user's base trajectory becomes longer, the increased portion is mostlikely on the highways. FIG. 8A also shows that Quadratic consistentlyoutperforms Linear. In popular areas, base trajectories and theircorresponding additive trajectories usually overlap each other, so thecloaking order does not have much impact on the cloaking results. FIG.8B again shows that the average cloaking range on popular roads is muchsmaller than that on unpopular roads. Also, as base trajectories becomelonger, the cloaking range increases on unpopular roads, but remainsalmost constant on popular roads.

3) Effect of the Number of Historical Trajectories:

This study investigates the impact of the number of trajectories in thefootprint database. We varied the number of trajectories in the databasefrom 100,000 to 300,000. For each simulation, we generated 200 basetrajectories, each averaged at 5000 meters with a deviation of 500meters. We set K=15 for each service request. The performance resultsare plotted in FIGS. 9A-9B. It is shown in FIG. 9A that the curve forBaseline is flat. This is not a surprise since this scheme uses only thecurrent position of mobile nodes for cloaking. As for Linear andQuadratic, both have better cloaking results when the database containsmore trajectories. Clearly, more historical trajectories means morechoices in selecting additive trajectory candidates for cloaking. Withthe same anonymity level, it can then find enough additive trajectoriesby searching in a smaller range for a base trajectory. Thus, thegenerated KATs have a smaller cloaking range. Since base trajectoriescan be added to the database for future cloaking, our proposedtechniques will generate better cloaking results as more footprints arecollected. This feature makes them especially attractive for large-scaleanonymization services. FIG. 9B shows that the increase of the number ofhistorical trajectories has a significant impact on the average cloakingrange on unpopular roads, but not on popular roads. On the expressway orstate roads, there is a sufficient number of footprints for cloaking,even when the database contains as few as 100,000 trajectories. Incontrast, for the unpopular roads, adding some new trajectories couldincrease their popularity substantially.

7. Feeling-Based Privacy Model

An anonymous location disclosed for an LBS may be correlated withrestricted spaces to identify a set of possible service requestors. Themore popular a spatial region is, the more difficult it is for anadversary to single out the true requestor. A user can specify herdesired level of protection by specifying a value of K: a spatial regiondisclosed on her behalf must have at least K different visitorsAlternatively, a user can specify a public region and request that herdisclosed location must be at least as popular as that space. An exampleof a public region can be some shopping mall in town. As compared tospecifying a number of K, it is much more intuitive for a user toexpress her privacy requirement by identifying a spatial region whichshe feels comfortable is reported as her location should she request anLBS from it. We refer to this approach as feeling-based privacymodeling.

When a location is disclosed for an LBS on a user's behalf, it must beat least the same popular as the public region she specifies. Theproblem now is how to measure the popularity of a spatial region. Thenumber of its visitor along is not sufficient to quantify itspopularity, because some people may have a dominant presence in thatspace. If an LBS is requested from an office, then the office staff ismore likely to be the service requestor, even if the office has manyvisitors. To address this problem, we borrow the concept of entropy fromShannon's information theory [24]. Suppose we can collect locationsamples from cellular phone users. These location samples, each called afootprint, can then be used to measure the popularity of a spatialregion as follows.

DEFINITION 2. Let R be a spatial region and S(R)={u₁, u₂, . . . , u_(m)}be the set of users who have footprints in R. Let n_(i)(1≦i≦m) be thenumber of footprints that user u_(i) has in R, and N=Σ_(i=1) ^(m)n_(i).We define the entropy of R as

${{E(R)} = {- {\sum\limits_{i = 1}^{m}\;{\frac{n_{i}}{N}\log\frac{n_{i}}{N}}}}},$and the popularity of R as P(R)=2^(E(R)).

The value of E(R) can be interpreted as the amount of additionalinformation needed for the adversary to identify the service user fromS(R) when R is reported as her location in requesting an LBS. Accordingto the above definition, we have 1<P(R)≦m. P(R) has the maximum value mwhen every user in S(R) has the same number of footprints in R. On theother hand, P(R) has the minimum value when a user in S(R) has N−m+1footprints in R while each of the rest has only 1. We have the followingtwo observations. First, P(R) is higher if m is larger. In other words,a region is more popular if it has more visitors. Second, P(R) has alower value if the distribution of footprints is more skewed. If someusers are dominant in the region, P(R) will be much less than m. In thiscase, R needs to be enlarged in order to have a required popularity.

Let R be a user's public region. When the user requests a sporadic LBS,where the request can be seen as an independent event, we can find acloaking box that 1) contains the user's current position, 2) has apopularity that is no less than P(R), and 3) is as small as possible,and then report this box as the user's location. When the user requestsa continuous LBS, a time-series sequence of cloaking boxes will bereported that form a trajectory. In this case, simply ensuring that eachcloaking box has a popularity no less than P(R) does not protect theuser's location privacy at her desired level. This is due to the factthat the adversary can narrow down the list of possible service users byfinding the common visitors of these cloaking boxes. T₀ prevent suchattack, we must use the footprints of the common set of users, insteadof all visitors of the regions, in computing the popularity of eachcloaking box. We define the popularity of a spatial region with respectto a given set of users as follows.

DEFINITION 3. Given a spatial region R, and a user set U={u₁, u₂, . . ., u_(m′)}⊂S(R), the entropy of R with respect to U is

${{E_{U}(R)} = {- {\sum\limits_{i = 1}^{m¢}\;{\frac{n_{i}}{N¢}\log\frac{n_{i}}{N¢}}}}},$where n_(i) is the numbers of footprints that u_(i) has in R, andN′=Σ_(i=1) ^(m¢)n_(i). The popularity of R with respect to U is P_(U)(R)=2^(E) ^(U) ^((R)).

When a sequence of cloaking boxes are generated on a user's behalf, wemust ensure that the popularity of each cloaking box with respect to thecommon set of visitors is no less than that of the user's public region.In other words, the trajectory formed by these cloaking boxes must be aP-Popular Trajectory (PPT), which is formally defined below:

DEFINITION 4. Let T={R₁, R₂, . . . , R_(n)} be a sequence of cloakingboxes generated for a user, and S(R_(i)) (1≦i≦n) the set of people whohave footprints in R_(i). We say T is the user's PPT if for each R_(i),it satisfies that (1) R_(i) covers the user's position at the time whenR_(i) is disclosed, and (2) P_(S)(R_(i))≧P(R), where S=∩_(1£i£n)S(R_(i)) and R is the public region specified by the user.Given a trajectory T={R₁, R₂, . . . , R_(n)}, we define its resolutionto be

${{T} = \frac{\sum\limits_{i = 1}^{n}\;{{Area}\mspace{14mu}( R_{i} )}}{n}},$where Area(R_(i)) denotes the area of box R_(i). For location privacyprotection, a trajectory formed by the location samples disclosed on auser's behalf must be a PPT. Meanwhile, its resolution needs to be asfine as possible to guarantee the quality of the required LBS services.Following, we focus on how to generate such a PPT for a user toentertain a continuous LBS.

8. Trajectory Cloaking

We assume mobile clients communicate with LBS providers through atrusted central location depersonalization server (LDS) managed by theclients' cellular service carriers. For LBSs that require userauthentication (e.g., for service charges), we assume anonymousauthentication (e.g., [11], [23], [20]) is used. The carriers offer thedepersonalization services as a value-added feature to their clients,and supply the LDS with an initial footprint database that containslocation samples collected from their clients (e.g., through regularphone calls). These location samples will be used to compute thepopularity of a spatial region and for trajectory cloaking. The databasewill be expanded with the location data obtained from mobile users intheir requests of LBSs.

We assume each client configures her privacy requirement by specifying apublic region. When a user requests an LBS, she also informs the LBDs atravel bound B, a rectangular spatial region that bounds her travelduring the service session. In response, the LDS randomly generates aservice session ID and contacts the service provider. After establishinga service session, the service user periodically reports her currentlocation to the LDS. For each location update, the LDS computes acloaking box which contains the service user's current location, andexports this box along with the session ID to the corresponding LBSprovider. The information received from the provider is then forwardedback to the service user. As mentioned early, to prevent restrictedspace identification, the trajectory created by the sequence of cloakingboxes must be a PPT that satisfies the user's privacy requirement. Thekey issue is how to find a common set of users for cloaking so that thetrajectory, which is undetermined, can have a resolution that is as fineas possible.

In the following subsections, we first describe the main data structureused for indexing the location samples stored in the footprint database,and then present a heuristic algorithm for trajectory cloaking.

8.1 Data Structure

We partition the network domain recursively into cells in a quad-treestyle. The partitioning stops when the size of cells becomes less than athreshold (our implementation sets each cell to be at least 100×100meter²). All the cells generated in the partitioning form a pyramidstructure as shown in FIG. 10. Suppose the partitioning stops at theh^(th) recursion, then the pyramid has a height of h. The top level inthe pyramid is level 1 and has only one grid cell that covers the wholenetwork domain. Each grid cell except the ones at the bottom level iscomposed of four cells at the next lower level, which we refer to as itschild cells.

Each cell at the bottom level h keeps a footprint table and a usertable. The footprint table stores the footprints the cell contains, andeach tuple of the table is a record of (uid, pos, tlink), where uid isthe identity of the mobile user that a footprint belongs to, pos is thecoordinates of a footprint, and tlink is a pointer that links to thecorresponding trajectory stored in the database. The user table recordsthe number of footprints a user has in the cell, and each tuple of thetable is a record of (uid,num), where num is the number of footprintsthat the user has in the cell. For each cell at the bottom level, wealso keep a user table, which is derived from the user tablescorresponding to its four child cells.

FIG. 10 illustrates the data structure 50 with a pyramid 52 having aplurality of levels or layers, including a first level 54, a secondlevel 56, a third level 58, and an h level 60. As previously discussed,each cell at the bottom level h keeps a cell or user table 62 and afootprint table 64. The footprint table 64 includes links tocorresponding historical trajectories stored in the database 66.

8.3 Generating PPT

We now discuss how to generate a PPT for a service user. Given theuser's public region R, the LDS computes its popularity P(R) using thecells at the bottom level that overlap with R. When the user makes thefirst location update, the server selects a set of users, which we willrefer to as a cloaking set. The footprints of this set of users are thenused for location cloaking whenever the service user makes a locationupdate.

8.3.1 Selecting Cloaking Set

It may first appear that we can determine the cloaking set, denoted asS, by finding the set of users who have footprints closest to thestarting point of the service user. This simple solution minimizes thesize of the first cloaking box. However, as the service user moves, theusers in S may not have footprints that are close to her currentposition. As a result, the size of the cloaking boxes may become largerand larger, making it difficult to guarantee the quality of LBS. Thus,when selecting the cloaking set, we should consider its affect on thecloaking of not only the user's first but all location updates in theLBS. But the challenge is that the service user's route is notpredetermined, and thus the LDS cannot figure out whose footprints willbe closer to the service user during her travel. To address thischallenge, our idea is to find those users who have visited most placesin the service user's travel bound B and use them to create the cloakingset. As these users have footprints spanning the entire region B, itwill help generate a PPT with a fine resolution.

We say a user is l-popular within B, if she has footprints in every cellat level l that overlaps with B. According to the pyramid structure,cells at level with a larger l have a finer granularity. This impliesthat given an l-popular user, the larger the value of l is, the morepopular the user is. FIG. 11 shows an example in which a network domainis partitioned into a 4-level pyramid (There are 1, 4, 16, 64 cells ateach level respectively from top to bottom). It also shows a travelbound B and the footprints inside it. The footprints in different colorsbelong to different users. u₁, u₂, and u₃ are three 2-popular userswithin B because they have footprints in the two cells at level 2 of thepyramid which overlap with B; u₂, u₃ are two 3-popular users within Bsince they have footprints in all four cells at level 3 that overlapwith B; only u₃ is 4-popular since she is the only one who hasfootprints in all the sixteen cells at level 4 that overlap with B.

Based on the above definitions, we now present a simple but effectivealgorithm that can find a cloaking set for trajectory cloaking. Thepseudo code is given in Algorithm 4. In this algorithm, the LDS sortsthe users in S(B) according to their popularity at level l, and selectsthe most popular users in S(B) as the cloaking set, starting from thebottom to top of the pyramid. Let C_(l) denote the set of cells at levell in the pyramid, C′_(l) the set of cells in C_(l) that overlap with B,and S_(l) the set of users who are l-popular within B. The LDS firstfinds S_(h). Since level h is the bottom level, these users are the mostpopular users in S(B). To find S_(h) (i.e., the users who have visitedall the cells in C′_(h)), the LDS simply joins the user tables of thesecells on column uid (line 6-7). Next, the LDS computes the popularity ofB with respect to S_(h) using their footprints in B. If the popularityP_(S) _(h) (B) is less than P(R), it means that cloaking with thefootprints of the users in S_(h) cannot provide the desired level ofprivacy protection for the service user. In this case, the LDS considersthe cells one level higher, i.e., level h−1 (line 9), and computesS_(h−1) and P_(S) _(h−1) (B) similarly. This procedure is repeated untilat some level l the popularity P_(S) _(l) (B) is no less than P(R). Thecomplexity of this algorithm is determined by the cost of computing userset S_(l) at each level from bottom to top. Let m denote the number ofusers in S(B) and k the number of cells in C′_(h). Then, the cost ofjoining two user tables is O(m), and the cost of joining user tables atbottom level (i.e., computing S_(h)) is O(k·m). According to the pyramidstructure, the number of cells at a certain level that overlap with B isabout one fourth of those at the next lower level. Thus, the total costof finding S_(l) on all levels is O(k·m).

Algorithm 4 SelectCloakingSet(P(R), B)  1: U < Q {U keeps the cloakingset}  2: l < h  3: while U S(B) and P_(U) (B) < P(R) do  4: {Get cellsat layer l overlapping with B}  5: C_(l) ^(′) < Overlap(C_(l,)B)  6:{Join user tables of C_(l) ^(′) by column uid}  7: T < Join (C_(l),^(′)uid)  8: U < S_(l) < T.uid  9: l < l − 1 10: end while 11: return U

The above algorithm checks the users level by level, from the bottom totop. If a user is l-popular within B, it must also be (l−1)-popularwithin B. Thus, each time the algorithm checks the cells at a higherlevel, the cloaking set is expanded to include more users. As long asP(R)≦P(B) (i.e., a user's public region is at most the same popular asthat of her travel bound), the algorithm will find a sufficient numberof visitors within B for the cloaking set. In the worst case, all usersin S(B) are included in the cloaking set. On the other hand, ifP(B)<P(R), the LDS does not need to find a cloaking set. It can simplycompute a spatial region that contains B and has a popularity no lessthan P(R), and always report this region as the user's location as longas it moves inside B.

8.3.2 Computing Cloaking Boxes

During a service session, the service user updates a time-seriessequence of locations. For each location update p, the LDS computes acloaking box b using the footprints of users in the cloaking set U. Wedevelop a heuristic algorithm which computes the cloaking box b as smallas possible, and ensures that P_(U)(b)≧P(R). The pseudo code is given inAlgorithm 5.

Given a location update p, the LDS first initializes the cloaking box btop which is the smallest cloaking box only containing the service userherself. The LDS also initializes a searching box b′ to the cell thatcontains p at level 1 where the cloaking set U is selected in Algorithm5, since it contains footprints of all users in the cloaking set. Then,for each user in U, the LDS gets the set of her footprints F_(u) whichare inside b′ but outside b, and in F_(u) the LDS finds the closest oneto p (line 7-8). Next, the LDS collects these footprints in set F, andcomputes the cloaking box b as the minimal bounding box (MBB) of thefootprints in F (line 11). If b already contains all footprints of U inb′, the LDS expands the searching box b′ by merging itself with itsadjacent cells at the bottom level (line 13-16). The above procedure isrepeated until P_(U)(b)≧P(R), and the resulting cloaking box b isreported as the service user's location to the external serviceprovider.

Algorithm 5 Cloak (p, P(R), U)  1: F < Q  2: l < the level where U isdetermined  3: b < p  4: b′ < the cell in C_(l) that contains p  5:while P_(U)(b) < O(R) do  6: for all u _(  ,  )U do  7: F_(u) < thefootprints of u in b′ − b  8: f_(u) < the closest footprint to p inF_(u)  9: F < F + {f_(u)} 10: end for 11: b < M B B(F) 12: if b containsall footprints of U in b′ then 13: {get cells at bottom level adjacentto b′} 14: C′ < Adjacent(b′,h) 15: {merging the cells in C′ with b′} 16:b′ < b′ ∪ C′ 17: end if 18: end while 19: return b

9. Performance Study

In this section, we evaluate the effectiveness of the proposed techniqueunder various conditions using location data synthetically generatedbased on a real road map. For comparison purpose, we have implementedtwo other approaches. The first one, which we refer to as Naive, assumesthe location updates made a service are independent to each other. Foreach location update, Naive just finds a cloaking box which satisfiesthe three conditions as previously described at the beginning of Section3, and reports it as the service user's location in her service request.Note that this scheme may not protect a user's location privacy at herdesired level when she makes a time-series sequence of location updates.The second approach is referred to as Plain hereafter. This schemedetermines the cloaking set for the service users by finding thefootprints closest to her start position. After fixing the cloaking set,Algorithm 5 is applied to compute the cloaking boxes for the serviceuser during her entire service session. To ease our presentation, wewill refer to our proposed technique as Advanced.

We modify the Network-based Generator of Moving Objects [4] to generatemobile nodes and simulate their movement on the real road map ofOldenburg, Germany, a city about 15×15 km². We extract four types ofroads from the road map, primary road (interstate expressway), secondaryroad (state road), connecting road and neighborhood road as defined incensus TIGER/Line [1]. In our simulation, mobile nodes change theirspeeds at each intersection, and the moving speed on a road follows anormal distribution determined by the road type. The mean speeds and thestandard deviations of moving speeds on all road types are listed inTable 3. We generate a footprint database that contains a certain numberof trajectories, and we assign them to 2000 users. The number oftrajectories each user has follows a normal distribution with a standarddeviation 0.1. These trajectories are indexed using the grid-basedapproach discussed in Section 3.1. For each simulation, we generate aset of LBS requests. Each service request contains a user's ID, a publicregion, and a travel bound. The start position are randomly selectedwithin the travel bound, and the service user moves randomly in thetravel bound, i.e., when she arrives at an intersection, she randomlychooses a direction to move on. We assume a user's travel distance isproportional to the size of the travel bound, and she makes a locationupdate every 100 meters when she moves. Other parameters used in ourstudy are given in Table 4. Unless otherwise specified, the defaultvalues are used.

In our study, we are mainly interested in the following two performancemetrics. One is cloaking area, defined to be the average area ofcloaking boxes in a cloaking trajectory. The other one is privacy level.Given a cloaking trajectory, we measure its protection level using theration between the average popularity of its cloaking boxes with respectto the common set of users who have visited all of them and thepopularity of the user specified public region. Clearly, the protectionlevel must be at least 1, otherwise the cloaking trajectory fails toprotect the service user's location privacy at the required level. Inthe following subsections, we report how the performance of the threetechniques is affected by various factors.

TABLE 3 Traffic parameters Road type Mean speed Standard deviationPrimary 100 km/h  20 km/h Secondary 60 km/h 15 km/h Connecting 45 km/h10 km/h Neighborhood 30 km/h  5 km/h

TABLE 4 Experiment Settings Parameter Range Default Unit Number of users2000 2000  unit Public region size  50-250 150 meter Trajectory databasesize 100K-300K 200K unit Travel bound size 2-6  4 km Travel distance 2-6 4 km Service request number  200 200 unit Minimum cell size 100 × 100100 × 100 meter²9.1 Effect of Privacy Requirement

This study investigates the impact of privacy requirement (i.e., thepopularity of the public region specified by a service user) on theperformance of the three techniques. We generated 300 service requests.Each request has a travel bound of a 4×4 km² square region, and thetravel distance of the corresponding user during her service session is4 km. Each service user specifies her public region as a square regionwhich contains her start position. The size of the public region,measured by the side length of the square, is varied from 50 to 250meters. The performance results are plotted in FIGS. 12A and 12B. FIG.12A shows that when the size of the public region increases, the averagecloaking area under all the three schemes increases. This is due to thefact that a larger public region is likely to contain more people'sfootprints and have a larger popularity. T₀ satisfy a higher level ofprivacy requirement, a cloaking box needs to be larger to include morepeople. This study also shows that Plain always has a much largercloaking area as compared to the other two approaches. This scheme doesnot take user popularity into consideration when selecting a user'scloaking set. When some unpopular users are selected in a cloaking set,the cloaking boxes generated for the future movement of a service userwill become larger in order to contain all users in the cloaking set. Onthe other hand, Native has the smaller cloaking area. This scheme doesnot consider the correlation of the cloaking boxes in a trajectory, justcloaking each location with a bounding box that is as small as possibleand has a popularity no less than that of the public region. The problemis, simply ensuring that each cloaking box satisfies the privacyrequirement does not protect the service user's privacy at her desiredlevel. This is confirmed in FIG. 12(b). It shows that the protectionlevel of Naïve is constantly lower than 1. As for Plain and Advanced,they both guarantee that the actual protection level is no less thanrequired.

9.2 Effect of Travel Distance

In this study, we investigated the impact of travel distance on theperformance of the three techniques. In each simulation run, we setpublic region as a 150×150 m² square, and generated 300 servicerequests. The travel distance is varied from 2 km to 6 km, andaccordingly the side length of travel bound is varied from 2 km to 6 km.The performance results are shown in FIGS. 12C and 12D. FIG. 12C showsthat under both Plain and Advanced, the average cloaking area increasesas the travel distance increases. However, Plain performs much worsethan Advanced. The reason behind is explained as follows. When thetravel distance is larger, the trajectory of the service user tends totraverse through a larger region. With an unpopular user in a cloakingset, it is more difficult to find their footprints close for eachlocation in the trajectory. Plain performs worse because in average itincludes more unpopular users in a cloaking set. On the other hand, thecloaking area under Native remains almost constant as the traveldistance changes. It is due to the fact that Native assumes eachlocation update is an independent event. For each location update, itsimply finds the nearest footprints to cloak. As such, the cloaking areais irrelevant to the number of location updates in the trajectory.Again, this approach cannot be used for location privacy protection whena user has to report her location periodically in a service session.FIG. 12D shows the protection level of Naive decreases as the traveldistance increases. Since each location update is cloaked independentlyin Naive, a longer cloaking trajectory tends to have a lesser number ofusers who have visited all cloaking boxes in the trajectory, and thushas a lower popularity with respect to this common set of users. Incontrast, the privacy level of neither Plain nor Advanced is muchaffected by the variance of travel distance.

9.3 Effect of Footprint Database Size

This study investigates the impact of the number of trajectories in thefootprint database on the performance. We varied the number oftrajectories in the database from 100,000 to 300,000. The performanceresults are plotted in FIGS. 12E and 12F. It is shown in FIG. 12E thatall schemes have better cloaking results when the database contains moretrajectories. Clearly, more historical trajectories mean that morefootprints are collected in a fixed spatial region. As a result, asmaller cloaking box may be populous enough to meet the privacyrequirement. By adding a service user's moving route to the database forfuture cloaking, our technique can generate better cloaking results.This feature makes it especially attractive for large-scale LBS thatconsist of a large number of users. FIG. 12F again shows that theprotection level of Naïve is constantly lower than 1. On the other hand,the protection level of both Plain and Advanced is always above 1.

10. Implementation

We have implemented an experimental system based on the techniquepresented in the previous sections. The prototype, called locationprivacy aware gateway (LPAG), has two software components, client andserver. Client is implemented in C# using Net Compact Framework 1.0. Itruns on Windows Mobile 2003 platform and we have tested it with twotypes of mobile devices, HP IPAQ 6515 and HP IPAQ 4310. The former is asmart phone with a built-in 4-channel GPS receiver. The devicecommunicates with the server through AT&T's GPRS wireless data services.As long as it is within the region covered by the carrier's servicenetwork, it can stay connected to the server which is located in ourlab. The other type of client device, namely HP IPAQ 4310, is a regularpocket PC which connects with the server through the university's campuswireless network, which limits its roaming area to within our campus. Tomake it position-aware, we bundle it with an external 16-channel GPSreceiver, which provides position information through a blue toothconnection. The server is implemented in C# using .Net Framework 1.0. Itmanages the historical location data and corresponding indices usingMySQL 5.0, and cloaks mobile clients' location updates using theproposed techniques when they request LBSs.

Our test of LPAG consists a location sampling during which we collectusers' footprints for location depersonalization. We create a number ofclient accounts, carry the devices and have a walk around the campus,during which the devices make periodic location updates to the sever.After a trajectory is collected, we randomly choose a client from theaccounts created before, assign the trajectory to the client, and saveit in the trajectory database in the server. In our testing of LPAG, wespecify a rectangular region in the campus as the public region, andhave a walk in the campus with a mobile device. During the walk, we senda sequence of queries to the server, each with our current position. Foreach query, the server generates a cloaking box using the proposedtechnique, and forwards it to the service provider. In response, theservice provider delivers all the messages whose bounding boxes overlapthe cloaking box to the server, and the server forwards to the clientonly the ones whose bounding box contains the client's current position.In the following subsections, we introduce our system's user interfacesand discuss the experimental results collected in our field tests.

10.1 Server and Client User Interface

FIG. 13A shows the server interface. Every time the server receives aquery from a client, it computes a cloaking box as the client's locationin requesting the service. Then, the server displays the cloaking boxand the client's position on the map. As the example shown in thisfigure, two clients and their cloaking boxes are displayed on the campusmap. The screen display 100 of a mobile device includes a first client102 in its corresponding cloaking box and a second client 104 in itscorresponding cloaking box.

When a mobile device is powered on, the client finds out the currentposition and then connects to the server. After initialization, thescreen shows a local map as its background and marks the client'sposition by a small face icon 108 (see FIG. 13B). A status area 106 isshown towards the bottom of the screen display. At the beginning of asession, the client can set the public region by clicking the touchscreen to specify its top-left corner and bottom-right corner, and embedthe public region in the query packet. In the example shown in FIG. 13B,the client specifies the library as her public region which is marked bythe rectangle. In our experiments, the travel bound is set as the wholecampus. Then, during the session, the client can choose to periodicallyupdate her location or manually update whenever she wants (see FIG.13C). As shown in FIG. 13C a screen display shows that latitude,longitude, time, port, and baud rate. In addition settings are shown forproviding updates to location information either automatically andperiodically or manually.

10.2 Experimental Results

We first examine the system resources used by our code running on mobiledevices.

CPU Utilization:

We measure the CPU utilization of our client code on the smartphoneusing Xda pps, which allows one to monitor the CPU usage of all theprocesses running on a smart device. When the device is idling with nomovement, the CPU utilization is about 1%, indicating that reading GPSposition (every one second) does not take much computation. When theclient moves around but does not make any location update, we observethat the CPU utilization is in between 4%-12%, as our code redraws theclient's position on the map. When the client communicates with theserver (e.g., location updates, message delivery), the CPU utilizationis in between 10%-25%.

Memory and Storage:

Our client executable is only 120 KB by itself. Since it is built on theNET Compact Framework 1.0 and OPENNETCF 1.4, additional 2.5 MB and 580KB files from the two platforms will be needed respectively. Whenrunning, our system has a memory footprint of 5.1 MB, which is less than10% of available main memory on HP IPAQ6515 (57.78 MB) and HP IPAQ4310(56.77 MB). On both devices, our code can run simultaneously with otherapplications such as media player and Internet explorer.

We also examine two performance metrics which affect the usability ofour system.

GPS Accuracy:

Because of position deviation of the GPS receiver, the position reportedto the server may be different from the actual position of a client. Ifthe position deviation is large, the bounding box computed by the servermay not contain the client's position, and the client may get the falsequery result (missing or downloading wrong messages). In ourexperiments, we have tested the accuracy of the two types of GPS in thecampus area. The smartphone we use has a built-in 4-channel GPS, whilethe external GPS bundled with the pocket PC has 16 channels. Tocalculate the position, a GPS receiver needs to have signals from atleast 4 satellites. In general, the more channels available, the moreaccurate position it can compute. Our tests show that the 16-channel GPShas 5 meters error in average and 8 meters error in maximum. While the4-channel GPS performs worse. It has 7 meters error in average and 14meters error in maximum. These tests indicate that in the worst case theserver should expand the boundary of the cloaking box by 15 meters toensure the cloaking box contains the client's actual position, and thebounding box of a message should not be smaller than 15×15 m.

Response Time:

The interval between the time a client sends a query and the time shereceives the query result is mainly composed of four parts: (1) the timeit takes to deliver the query from the client to the server, (2) thetime the server uses to computes the cloaking box, (3) the time for theserver to send the cloaking box to the service provider and receivescandidate messages from the service provider, (4) the time it takes todownload the resulting messages from the server to the client. Ourexperiments show that the server computes the cloaking box every fast,usually in less than 10 ms. In addition, the transmission speed betweenserver and service provider are also very fast (>4 MB/s), since they areconnected with a high speed LAN. The bottleneck is the communicationbetween the client and the server, i.e., part (1) and (4). Thesmartphone we use connects to our server via AT&T's GPRS, while thePocket PC connects to our server via our campus's WLAN. In our test, wecreate a number of messages, some with simple text messages (1-5 KB) andshort audio clips (10-30 KB), while the rest with video clips (100-300KB). Our tests show that for messages with simple text and audio clips,the smartphone and pocket PC can download them with a delay of less than1 second and 3 seconds, respectively; for the messages with video clips,the pocket PC has a minimal delay of 5 seconds while the smartphone hasa latency of more than 20 seconds. This study indicates that forcellular phones, our system is more appropriate for light-weightedmessages. Fortunately, this will not be a problem as cellular carriersprovide broadband wireless services.

11. Conclusion

According to one aspect, the present invention leverages historicallocation samples for location depersonalization. For eachlocation/trajectory reported for an LBS, we ensure that it has beenvisited earlier by some minimal number of users. An adversary may beable to identify all these users, but will not know who was there at thetime when the service was requested. As such, cloaking with footprintsmakes it possible to prevent the location information collected by theproviders of LBSs from being used to derive who's where at what time.

One method assume uniform distribution of footprints and may generate aKAA/KAT (e.g. an office) where some user has a dominant presence.Another method measures the anonymity level of a KAA/KAT using entropy[22][24], instead of the number of different users. In addition, someembodiments of the present invention provide on-the-fly cloaking.

Another aspect of the present invention uses a feeling-based model forlocation privacy protection. This model has two unique features. First,it allows mobile clients to configure their privacy preference based ontheir intuitive feeling. Instead of a number k, a client can specify apublic region which she feels comfortable if the region is reported asher location. Second, we borrow the concept of entropy from informationtheory and use it to evaluate the privacy level of a spatial region.This approach takes into account not only the number of users who visita spatial region, but also the frequency and duration of their visits.Based on this model, we investigate the problem of trajectory cloakingand propose a novel solution that is able to cloak a client's trajectoryon the fly. For performance study, we have implemented a prototype thatsupports location privacy-aware uses of LBSs. The system allows us toevaluate the effectiveness of the proposed techniques under variousconditions.

Therefore, a method for location depersonalization for location privacyprotection in location-based services has been disclosed. That which hasbeen described is merely exemplary. The present invention contemplatesnumerous variations, options, and alternatives fall within the spiritand scope of the invention.

12. References

The following references are cited throughout the text of thespecification. Each of these references is hereby incorporated in itsentirety.

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What is claimed is:
 1. A non-transitory computer readable medium bearingone or more instructions for providing location-based services to a userby cloaking a location using footprints comprising: receiving a locationassociated with a mobile node, wherein the location of the mobile nodecomprises a selection of a spatial region from the user; receiving ananonymity level associated with the location of the mobile node;computing a region containing the location of the mobile node and anumber of footprints based on the anonymity level, wherein each of thefootprints is from a different user and said footprints comprisehistorical location samples stored in an accessible database and saidnumber of footprints taken from the database; and providing the regionto a location-based service to thereby preserve anonymity of the mobilenode; wherein computing the region comprises determining a minimalbounding circle being computed with a polynomial-time algorithm.
 2. Themedium of claim 1, further comprising the instruction: adding afootprint associated with the location of the mobile node to thedatabase.
 3. The medium of claim 1, wherein the region is a circle. 4.The medium of claim 1, wherein the location is a user's public regionthat the user feels comfortable that the region is reported as currentlocation when the user is inside the region.
 5. The medium of claim 1,further comprising providing location privacy protection for the mobilenode.
 6. A mobile device for providing location-based services to a userby cloaking an instant location using footprints, the mobile devicecomprising: a cellular transceiver and a global positioning system (gps)receiver and wherein the mobile device configured to receive a selectionof a spatial region from the user; a computer associated with the mobiledevice for computing an anonymity level associated with the user,wherein said computer comprising a database comprising a plurality offootprints, wherein the footprints are different mobile devices'historical location samples; and wherein said computer configured tocompute a region containing the spatial region of the mobile device anda number of footprints from the database based on the anonymity level tothereby cloak when the user is within the region and to provide theregion to a location-based service to thereby preserve anonymity of themobile device; and wherein computing the region comprises determining aminimal bounding circle being computed with a polynomial-time algorithm.